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Open AccessArticle

Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem

by Juliana Bueno-Soler 1,† and Walter Carnielli 2,*,†
Faculty of Technology, State University of Campinas –UNICAMP, Campinas 13484-332, Brazil
Centre for Logic, Epistemology and the History of Science and Department of Philosophy, State University of Campinas—UNICAMP, Campinas 13083-859, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Julio Stern
Entropy 2016, 18(9), 325;
Received: 10 June 2016 / Revised: 9 August 2016 / Accepted: 19 August 2016 / Published: 7 September 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed. View Full-Text
Keywords: paraconsistency; probability; contradiction; consistency; logics of formal inconsistency paraconsistency; probability; contradiction; consistency; logics of formal inconsistency
MDPI and ACS Style

Bueno-Soler, J.; Carnielli, W. Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem. Entropy 2016, 18, 325.

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